If you mean arguments about programs, I handle them by avoiding them, or by trying to make a positive contribution. I got turned off of rational recovery in part because it seemed like one big argument, but honestly I also wasn't ready to do the work I needed to get sober at the time. I haven't looked into it in a long time.
The only program-related arguments I sometimes get into are kind of about arguing--the dogmatism of some people in my program (AA) and in many others turns away a lot of people who are looking for sobriety. If someone is getting sober in any remotely sane way, they deserve support; if they are staying sober, they deserve support and congrats; if they are lecturing others about the right way to get sober, they need to lighten the **** up, watch a few episodes of Sesame Street, and recall the timeless wisdom that, hey, not everyone is the same! People who claim you must be spiritual as they define it, in any program, are a case in point, but people who bash any program for any reason aren't doing a heck of a lot of good either.
Other arguments I've learned to handle a little better as a result of taking a long hard look at my old strategies (through working the steps). What am I really arguing for? Often my own vanity, or out of baseless fear. If I think in time (not always the case, to be sure), I can avoid arguments entirely, or at least avoid becoming too deeply absorbed in them. Sobriety allows me to be clearer going in and coming out of disagreements; a commitment to staying sober means not letting any disagreement provide me with an excuse to say **** it all to the world.
Gee, I sure am using a lot of ****ing asterisks today.